For the given functions f and g, find the requested function and state its domain.
-$\begin{array} { l }
f ( x ) = x + 6 ; g ( x ) = 3 x ^ { 2 } \ { Find } f + g
\end{array}$
A) $( f + g ) ( x ) = - 3 x ^ { 2 } + x + 6$; all real numbers
B) $( f + g ) ( x ) = 3 x ^ { 2 } - x - 6 ;$ all real numbers
C) $( f + g ) ( x ) = 3 x ^ { 2 } + x + 6 ; \{ x \mid x \neq - 6 \}$
D) $( f + g ) ( x ) = 3 x ^ { 2 } + x + 6$; all real numbers

Question

For the given functions f and g, find the requested function and state its domain.
-$\begin{array} { l } 
f ( x ) = x + 6 ; g ( x ) = 3 x ^ { 2 } \  { Find } f + g
\end{array}$ 
A) $( f + g ) ( x ) = - 3 x ^ { 2 } + x + 6$; all real numbers
B) $( f + g ) ( x ) = 3 x ^ { 2 } - x - 6 ;$ all real numbers
C) $( f + g ) ( x ) = 3 x ^ { 2 } + x + 6 ; \{ x \mid x \neq - 6 \}$
D) $( f + g ) ( x ) = 3 x ^ { 2 } + x + 6$; all real numbers

Quizplus · Accepted Answer

To find $f + g$, you add the functions $f(x) = x + 6$ and $g(x) = 3x^2$ together, resulting in $3x^2 + x + 6$. Both functions are polynomials, which are defined for all real numbers, so the domain of $f + g$ is all real numbers.

For the Given Functions F and G, Find the Requested f(x)=x+6;g(x)=3x2Findf+g\begin{array} { l } f ( x ) = x + 6 ; g ( x ) = 3 x ^ { 2 } \\ { Find } f + g\end{array}f(x)=x+6;g(x)=3x2Findf+g​

For the Given Functions F and G, Find the Requested $\begin{array} { l } f ( x ) = x + 6 ; g ( x ) = 3 x ^ { 2 } \\ { Find } f + g\end{array}$